Upon receipt of an application, the division shall fix a time and place of a hearing thereon and shall give notice of the pendency of the application and of the time and place of the hearing thereon to the applicant, to the mayor of each city and the president of the town council of each town in or through which the applicant desires to operate, and to any common carrier operating over any portion of a route or over a route substantially parallel thereto, and shall give a public hearing upon the petition. Any town or city within which or between which, and any other town or city to which a common carrier is furnishing service, may, at any time after the certificate of public convenience and necessity has been issued, bring a written petition to the division in respect to routes, fares, speed, schedules, continuity of service, and the convenience and safety of passengers and the public. Thereupon, the division shall fix a time and place for a hearing upon the petition and shall mail a notice thereof to the parties in interest and give such other notice thereof as the division may deem proper by advertisement. The division may revoke or amend any certificate.